Comparison of Cascade and Feedforward-Feedback Controllers for Temperature Control on Stirred Tank Heater Systems

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Comparison of Cascade and Feedforward-Feedback
Controllers for Temperature Control on Stirred Tank
Heater Systems
Bhakti Yudho Suprapto
Departement of Electrical
Engineering
Universitas Sriwijaya
Jl Raya Palembang-Prabumulih
Km. 32 Inderalaya, South of
Sumatera, Indonesia
bhakti@ft.unsri.ac.id
Ike Bayusari
Departement of Electrical
Engineering
Universitas Sriwijaya
Jl Raya Palembang-Prabumulih
Km. 32 Inderalaya, South of
Sumatera, Indonesia
ikebayusari@yahoo.co.id
Caroline
Departement of Electrical
Engineering
Universitas Sriwijaya
Jl Raya Palembang-Prabumulih
Km. 32 Inderalaya, South of
Sumatera, Indonesia
caroline.herry@yahoo.com
Muhammad
Departement of Electrical
Engineering
Universitas Sriwijaya
Jl Raya Palembang-Prabumulih
Km. 32 Inderalaya, South of
Sumatera, Indonesia
fadilassegaf@hotmail.com
Abstract— The temperature control in stirred tank heater
(STH) systems is important, especially since the equipment is
utilized in a wide variety of industries such as oil and gas. However,
within the current STH control process there is often a small
disturbance which adversely affects the overall process and it is
quite difficult to solve with a regular feedback configuration. Many
researchers have applied cascade and feedforward control
configurations to solve this problem. Therefore, this paper
discusses a comparison of cascade and feedforward-feedback
control configurations in maintaining and regulating temperature
in the STH. The results show that a cascade controller
configuration performs better in various test conditions than a
feedforward-feedback controller.
Keywords—cascade; control; feedforward-feedback; PID;
stirred tank heater
I.
I
NTRODUCTION
The stirred tank heater (STH) is one of the most widely
used types of equipment in the industrial today. The chemical,
oil, and gas industries are particularly dependent on STH
technology. At the most basic level, the STH is a tank that
mixes materials and applies heat to produce a new product. The
use of heat is key to the reactions taking place within the STH.
Therefore, temperature control becomes an important factor
and must be considered when studying ways to produce a good
product or otherwise improve the process. Temperature control
is usually achieved by controlling a valve which releases fuel;
opening the fuel release valve results in higher temperatures
while closing the valve has the opposite effect. Temperature
control can also be regulated by controlling the flow of heated
materials such as gas or steam into or around the STH.
Temperature control for STH equipment has been extensively
studied including using Proportional Integral Derivative
(PID)[1], Proportional Integral (PI)[2], dan fuzzy PID[3]
controllers. Other studies reported using a combination of
computational intelligent methods to optimize PID control
parameters [4]. This controller has been able to solve general
problems of temperature control. However, in the process of
controlling the temperature, there is often a coincide change in
pressure of gas or steam. This change in pressure will interfere
with the attempts to control temperature, although the effect
does not directly interfere with the system. As a result of this
pressure change, the temperature will also change. To solve
this problem, the controller configuration is modified by
adding a secondary controller which compensates for the initial
pressure changes then maintain the correct temperature. In this
configuration, the addition of a secondary controller system
will also add a secondary sensor to determine the disturbance
condition faster than the controlled variable. This approach is
called the cascade control system [5]
.
The advantages of this
cascade controller configuration, i.e. the ability to increase the
response speed of the primary controller by increasing the
response from the secondary controller. If there is a disturbance
then the secondary controller will overcome the interference
directly.[5][6].
Other disturbances that need to be compensated for during
the process within the STH include an error in the modeling
and the existence of unmeasurable disturbance. To overcome
any modeling error a feedback controller can be used, while to
overcome the immeasurable disturbance on the sensor a
feedforward controller can be used. Feedforward and feedback
controllers can be combined in different ways. In the controller
configuration, the feedforward and feedback outputs are
summed, where the summed signal will be sent to the
controller. Such control is commonly called the feedforward-
feedback system[5]. The advantages of the feedforward-
feedback controller configuration are: the controlled variable
does not have to be measurable; the error correction is
immediate when there is a disturbance, and any actions and
changes in this configuration do not affect the stability of the
process[5][7][8].
Both controller configurations also have the disadvantage
i.e. adding to the cost of the equipment, due to the addition of
controllers and sensors. However, this addition is proportional
to the performance shown by these two control configurations
in overcoming the disturbance. This paper compares both types
of control configurations in STH temperature control. Both
types of control configurations will be seen their response of

control to handle undesirable temperature changes as well as
tracking disturbance.
This paper is structured as follows: Section 1—
Introduction, explaining the problem, current research, and
objectives of this paper; Section 2—Stirred Tank Heater
modeling; Section 3—Research Method, describing the
controller configuration method used in this paper; Section
4—Results, including an Analysis of the experiment that has
been done; and Section 5—Conclusion.
II. S
TIRRED
T
ANK
H
EATER
M
ODELLING
STH is a common type of industrial equipment that is
designed to mix certain materials at a specific temperature. The
contents of the STH must be stirred so that the mixture is
evenly distributed in order to consistently produce a particular,
high-quality product. In addition to blending the ingredients as
they mix, the stirrer also serves to prevent the mixed material
from being frozen or becoming too thick. Heat is obtained from
heaters, or from steam or gas. The heat conductively moves to
the substances contained in the STH tank through the coil wall.
The STH work process can be seen in Fig. 1, where
temperature (T
i
) and flow (F
i
) at the input are assumed to be
constant. The output is the new product, which is also at a
specific flow and temperature. The temperature of the tank is
maintained at a setpoint. Heat (Q) is used to keep the
temperature constant. Temperature control is performed to
regulate the heat by adjusting the valve controlling the flow of
steam or gas.
Based on Fig. 1 it is assumed that the heater has been
worked and the liquid temperature is kept constant (T
S
). The
fluid volume must also be maintained at a constant state, a
value of V. The mathematical equation model pertaining to the
STH can be defined using the law of total energy balance in
the process tank by the equation:
0 = FρC (T
I,
s – T
S
) + Q
S
(1)
Or
0 = WC (T
I,S
– T
S
) + Q
S
(2)
Where C is the heat of type (KJ/Kg
o
C), T
S
is the steady state
of the output temperature (
o
C), T
IS
is the steady state of the
input temperature (
o
C), ρ is the liquid type density (Kg/m
3
), F
is the fluid flow rate (m
3
/s), and W is the mass flow rate
(W=F. ρ) (Kg/s).
Fig. 1. Stirred Tank Heater Work Diagram
If T
I
suddenly increases and if Q
S
(energy in steady state
condition) has no change, then the energy balance around the
tank is::[4][5]
(3)
(4)
Where M = V. ρ and M are the tank mass (Kg), ρ is the
density of the species (Kg / m
3
), and V is the volume of the
vessel (m
3
). The design of this heating system uses the same
working principle as a steam-heat modeling process, where
input pressure is controlled. In this modeling process, the
heater uses gas, which is sent to the stove to burn. So the main
factor on the heater is the gas pressure output. The pressure of
the gas is then set as the temperature of fire (
T
A
) through the
adjustment of the thermodynamic relationship.
T
A
= f ( P
G
)
(5)
So the energy balance is [4]
MC =
WC(T
I
– T)
+
h
P
A
P
(T
D
-T) (6)
M
D
C
D
=
K
A
A
A
-
h
P
A
P
(T
D
-T)
(7)
Where:
• K
A
is the Aluminum Conductivity (W / m
o
C)
• C
D
is the Hearth type of wall (KJ / Kg
o
C)
• A
P
= A
A
is the cross-sectional area (m2),
• T
A
is the temperature in gas (Fire) (
o
C),
• h
P
is the heat transfer coefficient W / m2
o
C), MD is
wall mass (Kg),
• T
D
is Tank wall temperature (
o
C),
• X is reactor tank thickness (m).
Based on the law of energy equilibrium, which stated that the
energy change in a system is equal to the amount of energy
entering the system minus the amount of energy going out of
the system, then equation (8), as follows[4]
=
ρFC(T
I
– T
ref
) – ρFC(T-T
ref
) + Q
(8)
or
=
WC(T
I
– T
ref
) – WC(T-T
ref
) + Q
(9)
The mathematical equation (3) can be developed from the
dynamic model equations of the STH heating system, i.e. (8)
and (9)[4].
MC = WC(T
I
– T) + h
P
A
P
(T
D
– T) (10)
M
D
C
D
= K
A
A
A
– h
P
A
P
(T
D
-T) (11)
Assuming the dynamic conditions in equation (11) can be
ignored, it is assumed that the tank wall value of temperature
or temperature (T
D
) equals the temperature or temperature of
the burning gas (T
A
). So equation (11) becomes: [4]
T
D
= (12)
Substituting into equation (3) will produce,

VρC = WC(T
I
) – WC(T) + UA (T
A
– T) (13)
Since the T output variables, UA is a multiplication of heat
transfer coefficient (h) to the cross-sectional area (A), and the
T
I
and P
G
input variables are still nonlinear, the variables are
converted into a linear form by deviation of variables,
resulting in [4]
WCT
I,S
=
ƒ
(WCT
I,S
) + WC(T
I
-T
I,S
) (14)
UA(P
G
– T) =
ƒ
(UA(P
G,S
– T
S
)) + UA(P
G
– P
G,S
) – (T-T
S
) (15)
-WCT = -
ƒ
(WCTS) – WC(T - T
S
) (16)
The steady state value is
0 = WCT
I,S
–WCT
S
+ UA(P
G,S
– T
S
) (17)
After the linearization values are known, the linear equations
(14), (15), and (16) are fed into (13). Substitution with (17)
then obtains the deviation equation of the variable below.[4]
VρC = WC(T
I
– T
I,S
) – WC(T-T
S
) + UA((P
G
– P
G,S
) – (T-T
S
))
(18)
or
VρC = WCT
I
’ – WCT
’
+ UA(P
G’
– T
’
) (19)
By doing a Laplace transform, generates:
VρC sT’(s) = WCT
I
’(s) – WCT’(s) + UA(P
G
’(s) – T’(s)) (20)
Changing into the transfer function obtains:[4]
T’(s) = T
I
’(s) + P
S
’(s) (21)
The transfer function of the control valve can be seen in the
following equation:[4]
=
(22)
Where K
CV
represents the total gain of the control valve, cv
denotes the constant time of the control valve (s), P
S
represents
the output signal from the controller (mA), P
GS
represents the
flow of LPG gas flowing through the valve (psi).
Based on the transfer function equation, the temperature
control block diagram of the STH is seen in Fig.2. where the
actuator is a control valve that will allow gas or steam to flow
in the STH model. The setpoint is the standard temperature to
be maintained and kept constant. The stirring speed of the
stirrer’s driving motor is also made constant. This control is a
closed loop. However, an issue arises if there is any
disturbance in the pressure of gas or steam, which directly
affects the temperature. Resolving this required proper
controller configuration.
Fig. 2. Block Diagram of Temperatur Control of The Stirred Tank Heater
III. C
ONTROLLER
C
ONFIGURATION
The controller which was used in this paper is the
Proportional Integral Derivative (PID) controller because it is
reliable, simple, and widely used throughout various industries.
However, the configuration will compare the performances
between cascade and feedforward.
Fig. 3. Block Diagram of Cascade Control
A. Cascade
The block diagram of the controller with this cascade
configuration can be seen in Fig. 3. In this controller, there are
two feedback paths in the cascade control system, thus forming
two loop controls, namely the outer loop which is the primary
loop (or master), and the inner loop which is the secondary
loop (or slave). The master or primary loop controls the
primary variable process (fluid temperature process), while the
slave or secondary loop controls the process of secondary
variables (vapor or gas pressure).
The cascade controller is chosen because there are several
reasons such as the output response of the single control is not
as expected, there is the addition of a secondary variable in the
control of the plant, which is added as a plant control, can
overcome the disturbance.
B. Feedforward-feedback
In this STH control system, if there is change of load from
the plant while the flow of steam or gas is constant, so it will be
used a feedback control system. But if the load changes happen
too quickly, then another type of control system becomes
necessary. Because conventional feedback paths need to "see"
errors before performing corrective actions, a standard
feedback system will not be able to handle the load well if the
load change frequency is too fast. Therefore, the design of the
feedforward system as shown in Fig. 4 is based on process
requirements, reducing the large loads that can disrupt the
output process. The ultimate design of the system is left up to
the designer because it is expected that a holistic, streamlined
design will be able to reduce the interaction between
feedforward and feedback (FFFB).
Fig. 4. Block Diagram of the Feedforward-feedback Control

IV. E
XPERIMENT
R
ESULT
The purpose of this paper is to compare the configurations
of the cascade and feedforward-feedback controllers. Both of
these configurations use PID controllers as both primary and
secondary controllers. The cascade controller has a response
when given setpoint temperature of 90°C. As shown in Fig. 5,
the resulting overshoot value is 12.1%, the rise time is 1.075
seconds. The settling time value is 25.45 seconds, and the
steady state error is 0% and the resulting offset value is 0.
Fig. 5. The response of Cascade Control with setpoint
Then it tested the disturbance in the form of a changing
setpoint as seen in Fig. 6. This test obtained the results of
overshoot values of 12.1%, 4.64%, 3.83%, 3.24% and 0.2%.
The average overshoot generated is 4.8%. The time rise results
are 0.2836 seconds, 0.28 seconds, 0.3 seconds, 0.3 seconds and
0.3 seconds. This results in an average rise time of 0.292
seconds. The settling time value results are 24.4 seconds, 21.73
seconds, 22.1 seconds, 21.1 seconds and 20.6 seconds. This
yields an average required settling time of 21.98 seconds. The
steady state error is 0% and the offset value is 0. These results
indicate the cascade control system on the stirred tank heater
can work well when used with changing set-point conditions.
This is evidenced by low overshoot value, fast rise time and
settling time and 0% steady state error. This proves an STH
will work well under these conditions.
Fig. 6. The response of Temperature Control of STH using Cascade Control
with Tracking Set-point
Fig. 7. The response of Temperature Control of STH using FFFB with
setpoint
Then, comparison tests were run using the FFFB
controller, again with both a single setpoint and a tracking
setpoint. Based on the output response generated in Fig 7, it
can be seen that the FFFB controller was effective for single-
setpoint conditions. The resulting overshoot value is 0.68%,
the rise time is 3.691 seconds, the settling time is 31.88
seconds, the steady state error is 0% and the offset value result
is 0. This response is very good, the overshoot is very small,
almost 0%, the rise time is fast, the settling time is also quite
good and the steady state error is 0%. This proves that the
FFFB control system is good enough to overcome the existing
issues.
Fig. 8. The response of Temperature Control of STH using FFFB with
Tracking Set-point
However, in Fig.8, the results of the FFFB configuration
with a changing setpoint were not as promising. The resulting
overshoot value is 22.8%, 13%, 10.6%, 9.01% and 5.6%, so
the average overshoot generated is 12.2%. The time rise
results were 1.322 seconds, 3.34 seconds, 3.3 seconds, 3.3
seconds and 3.3 seconds, which yields an average rise time
equal to 2.91 seconds. Settling time values were 56.11
seconds, 51.8 seconds, 63.6 seconds, 51.8 seconds and 63.2
seconds, so the average settling time required is 57.3 seconds.
The steady state error is 0% and the resulting offset value is 0.
The resulting response is good enough, the overshoot is low,
the rise time is fast and the steady state error is 0%, but the
settling time is not very fast since the average was 39.81
seconds.

Based on the response generated by these two
configurations, it can be seen that for conditions where the
temperature setpoint is desired to be kept constant, the cascade
controller has a smaller rise time and faster settling time than
the FFFB controller. Therefore, the cascade is better than
FFFB even though the overshoot generated is quite high. The
comparison of response both of this controller can be seen in
table 1. Although better, the cascade has its drawbacks; with
its high overshoot, equipment may be adversely affected. In
the cascade configuration, responses are accelerated due to the
direct influence of the secondary controller. Anticipating the
influence of pressure changes on steam or gas in the heater
results in a high overshoot in an attempt to reach the new
setpoint temperature. In the FFFB controller tests, under fixed
setpoint conditions, the results indicate that the controller tries
simply to approach the setpoint. Therefore, adding FFFB
controllers is quite effective in minimizing overshoot. This
ensures the safety of the equipment, but the time to reach a
stable temperature exceeds the amount of time needed by the
cascade. Similarly, when comparing the results of the test with
changing setpoints, the cascade configuration proved to be the
better choice because the rise time, overshoot and settling time
all were lower than the FFFB. The only advantage to FFFB in
the conditions introducing disorder by testing setpoint changes
is that FFFB can eliminate the overshoot and thereby reduce
the risk of equipment damage compared to the cascade.
TABLE I. C
OMPARISON OF
C
ASCADE AND
F
EEDFORWARD
-F
EEDBACK
C
ONTROLLER RESPONSE WITH SETPOINT
Controller Rise time
(second)
Overshoot
(%)
Settling time
(second)
Error Steady
state (%)
Cascade
with setpoint
1.575 12.1 25.45 0
FFFB with
Setpoint
3.691 0.68 31.88 0
V. C
ONCLUSIONS
Based on the experiments and the tests that have been
conducted, the cascade is better than the feedforward-feedback
control system for a stirred tank heater (STH). The biggest
advantage is that the cascade system generates the lowest rise
time and settling time values. The cascade also has better
results than the feedforward-feedback under changing setpoint
conditions, based on the following factors: overshoot
situations, rise time, and lower settling time. Future jobs will
test other types of controllers such as PI and fuzzy logic, to
develop more and better controllers for STH systems.
R
EFERENCES
[1] A. S. Rajagopalen, “Identification of an effective controller for a
stirred tank heater process,” Int. J. Eng. Adv. Technol., vol. 3, no. 1,
pp. 271–279, 2013.
[2] S. Sehgal and V. Acharya, “Design of PI controller for continuous
stirred tank heater process,” in 2014 IEEE Students’ Conference on
Electrical, Electronics, and Computer Science, SCEECS 2014,
2014.
[3] K. V and G. D. G, “Comparative Analysis of PID and Fuzzy PID
Controller Performance for Continuous Stirred Tank Heater,” Indian
J. Sci. Technol., vol. 8, no. 23, pp. 1–7, 2015.
[4] N. I. Septiani, I. Bayusari, C. Caroline, T. Haiyunnisa, and B. Y.
Suprapto, “Optimization of PID control parameters with genetic
algorithm plus fuzzy logic in the stirred tank heater temperature
control process,” in ICECOS 2017 - Proceeding of 2017
International Conference on Electrical Engineering and Computer
Science, 2017, pp. 61–66.
[5] D. E. Seborg, T. F. Edgar, D. A. Mellichamp, and F. J. Doyle III,
Process Dynamics, and Control. 2011.
[6] I. Kaya, N. Tan, and D. P. Atherton, “Improved cascade control
structure for enhanced performance,” J. Process Control, vol. 17,
no. 1, pp. 3–16, 2007.
[7] M. Malek, P. Makys, and M. Stulrajter, “Feedforward Control of
Electrical Drives - Rules and Limits.,” Power Eng. Electr. Eng., vol.
9, pp. 35–42, 2011.
[8] J. L. Guzmán, T. Hägglund, M. Veronesi, and A. Visioli,
“Performance indices for feedforward control,” J. Process Control,
vol. 26, pp. 26–34, 2015.